Solve (4x^-8)^3/2

To solve the expression (4x^-8)^(3/2), we need to follow the order of operations.

First, let's simplify the exponent 3/2 by raising the base (4x^-8) to the power of 3 and then taking the square root.

(4x^-8)^(3/2) = (4x^-8)^3 ^1/2

Now, let's raise the base 4x^-8 to the power of 3:

(4x^-8)^3 = 4^3 * (x^-8)^3 = 64 * (x^(-8 * 3)) (applying the power of a product rule) = 64 * x^(-24)

Next, let's take the square root of the result:

(64 * x^(-24))^(1/2) = (64^(1/2)) * (x^(-24 * (1/2))) = 8 * (x^(-12)) (since 64^(1/2) is equal to 8)

Therefore, (4x^-8)^(3/2) simplifies to 8 * x^(-12).